Apparatus and methods employing liquid-impregnated surfaces

ABSTRACT

In certain embodiments, the invention is directed to apparatus comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, and methods thereof. In some embodiments, one or both of the following holds: (i) 0&lt;ϕ≤0.25, where ϕ is a representative fraction of the projected surface area of the liquid-impregnated surface corresponding to non-submerged solid at equilibrium; and (ii) Sow(a)&lt;0, where Sow(a) is spreading coefficient, defined as γwa−γwo−γoa, where γ is the interfacial tension between the two phases designated by subscripts w, a, and o, where w is water, a is air, and o is the impregnating liquid.

RELATED APPLICATIONS

This application is a 35 U.S.C. 371 National Stage of InternationalApplication No. PCT/US2013/070827, filed on Nov. 19, 2013, whichdesignated the U.S. and which claims the benefit of U.S. ProvisionalPatent Application No. 61/827,444, which was filed on May 24, 2013 andU.S. Provisional Patent Application No. 61/728,219, which was filed onNov. 19, 2012, each of which is incorporated herein by reference in itsentirety.

TECHNICAL FIELD

This invention relates generally to non-wetting and low adhesionsurfaces. More particularly, in certain embodiments, the inventionrelates to non-wetting, liquid-impregnated surfaces that are engineeredto eliminate pinning and/or to either avoid or induce cloaking.

BACKGROUND

The advent of micro/nano-engineered surfaces in the last decade hasopened up new techniques for enhancing a wide variety of physicalphenomena in thermofluids sciences. For example, the use of micro/nanosurface textures has provided nonwetting surfaces capable of achievingless viscous drag, reduced adhesion to ice and other materials,self-cleaning, and water repellency. These improvements result generallyfrom diminished contact (i.e., less wetting) between the solid surfacesand adjacent liquids.

One type of non-wetting surface of interest is a superhydrophobicsurface. In general, a superhydrophobic surface includesmicro/nano-scale roughness on an intrinsically hydrophobic surface, suchas a hydrophobic coating. Superhydrophobic surfaces resist contact withwater by virtue of an air-water interface within the micro/nano surfacetextures.

One of the drawbacks of existing non-wetting surfaces (e.g.,superhydrophobic, superoleophobic, and supermetallophobic surfaces) isthat they are susceptible to impalement, which destroys the non-wettingcapabilities of the surface. Impalement occurs when an impinging liquid(e.g., a liquid droplet or liquid stream) displaces the air entrainedwithin the surface textures. Previous efforts to prevent impalement havefocused on reducing surface texture dimensions from micro-scale tonano-scale.

Although not well recognized in previous studies of liquid-impregnatedsurfaces, the impregnating liquid may spread over and “cloak” thecontacting liquid (e.g., water droplets) on the surface. For example,cloaking can cause the progressive loss of impregnating liquid throughentrainment in the water droplets as they are shed from the surface.

Frost formation is another problem affecting a large variety ofindustries, including transportation, power generation, construction,and agriculture. The effects of frosting may lead to downed power lines,damaged crops, and stalled aircrafts. Moreover, frost and iceaccumulation significantly decreases the performance of ships, windturbines, and HVAC systems. Currently used active chemical, thermal, andmechanical techniques of ice removal are time consuming and costly inoperation. Development of passive methods preventing frost and iceaccretion is highly desirable. Hydrophobic surfaces have a high energybarrier for ice nucleation and low ice adhesion strength and, ifproperly roughened on the nano- and/or micro-scales, can repel impact ofsupercooled water droplets. However, the anti-icing properties ofhydrophobic as well as superhydrophobic surfaces are negated once thesurfaces are frosted. Frost formation and ice adhesion can also bereduced by addition of a liquid or grease onto the working surface. Forexample, ice adhesion to aircraft surfaces is significantly reducedthrough application of silicone grease, and frost formation can beprevented on exterior of freezers and heat exchangers coated with a 100μm porous layer infused with propylene glycol antifreeze. However, inboth of these cases the non-solid phases are sacrificial and can leakinto the surroundings causing significant environmental problems.

There is a need for non-wetting surfaces that are robust and/or deliveroptimal non-wetting properties and resist frost formation.

SUMMARY OF THE INVENTION

Described herein are non-wetting surfaces that include a liquidimpregnated within a matrix of micro/nano-engineered features on thesurface, or a liquid filling pores or other tiny wells on the surface.In certain embodiments, compared to previous non-wetting surfaces, whichinclude a gas (e.g., air) entrained within the surface textures, theseliquid-impregnated surfaces are resistant to impalement and frostformation, and are therefore more robust.

Impregnating fluids that cover the tops of the matrix of solid featuresoffer a non-wetting benefit. However, at equilibrium, the impregnatingliquid may not cover the tops of solid features (e.g., microposts ornanograss) of the surface without being continually replenished.Furthermore, while certain impregnating fluids do cover the tops ofsolid features, offering a non-wetting benefit, they often exhibitcloaking, and the impregnating fluid is depleted unless replenished.

It is discovered that liquid-impregnated surfaces can be engineered toprovide resistance to impalement and to provide non-wettability, withoutrequiring replenishment of impregnating fluid to make up for liquid lostto cloaking, and without requiring replenishment of impregnating liquidto maintain coverage over the tops of the solid features.

In one aspect, the invention is directed to an article comprising aliquid-impregnated surface, said surface comprising an impregnatingliquid and a matrix of solid features spaced sufficiently close tostably contain the impregnating liquid therebetween or therewithin,wherein one or both of the following holds: (i) 0<ϕ≤0.25, where ϕ is arepresentative fraction of the projected surface area of theliquid-impregnated surface corresponding to non-submerged solid (i.e.,non-submerged by the impregnating liquid, e.g., can be “non-submerged”and still in contact with water) at equilibrium (e.g., where equilibriumcan encompass pseudo-equilibrium); and (ii) S_(ow(v))<0, where S_(ow(v))is spreading coefficient, defined as γ_(wv)−γ_(wo)−γ_(ov), where γ isthe interfacial tension between the two phases designated by subscripts,said subscripts selected from w, v, and o, where w is water, v is vaporphase in contact with the surface (e.g., air), and o is the impregnatingliquid.

In some embodiments, 0<ϕ≤0.25, or 0.01<ϕ≤0.25, or 0.05<ϕ≤0.25. In someembodiments, S_(ow(v))<0.

In some embodiments, the impregnating liquid comprises at least onemember selected from the group consisting of silicone oil, propyleneglycol dicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin(PAO), synthetic hydrocarbon cooligomer, fluorinated polysiloxane,propylene glycol, tetrachloroethylene (perchloroethylene), phenylisothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene,o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene,acetylene tetrabromide, 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl)imide (BMIm), tribromohydrin(1,2,3-tribromopropane), ethylene dibromide, carbon disulfide,bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquidpetrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbondisulfide, phenyl mustard oil, monoiodobenzene,alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butylalcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleicacid, and amyl phthalate.

In some embodiments, the solid features comprise at least one memberselected from the group consisting of a polymeric solid, a ceramicsolid, a fluorinated solid, an intermetallic solid, and a compositesolid. In some embodiments, the solid features comprise a chemicallymodified surface, coated surface, surface with a bonded monolayer. Insome embodiments, the solid features define at least one member selectedfrom the group consisting of pores, cavities, wells, interconnectedpores, and interconnected cavities. In some embodiments, the solidfeatures comprise at least one member selected from the group consistingof posts, nanoneedles, nanograss, substantially spherical particles, andamorphous particles. In some embodiments, the solid features have arough surface (e.g., the solid features have a surface roughness>50nm, >100 nm, e.g., and also <1 μm). In some embodiments, the roughsurface provides stable impregnation of liquid therebetween ortherewithin, such that θ_(os(v),receding)<θ_(c), where θ_(c) is criticalcontact angle.

In some embodiments, the liquid-impregnated surface is configured suchthat water droplets contacting the surface are not pinned or impaled onthe surface and have a roll-off angle α of less than 40°. In someembodiments, the water droplets have a roll-off angle α of less than35°, less than 30°, less than 25°, or less than 20°.

In another aspect, the invention is directed to an article comprising aliquid-impregnated surface, said surface comprising an impregnatingliquid and a matrix of solid features spaced sufficiently close tostably contain the impregnating liquid therebetween or therewithin,wherein one or both of the following holds: (i) θ_(os(w),receding)=0;and (ii) θ_(os(v),receding)=0 and θ_(os(w),receding)=0, whereθ_(os(w),receding) is receding contact angle of the impregnating liquid(e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in thepresence of water (subscript ‘w’), and where θ_(os(v),receding) isreceding contact angle of the impregnating liquid (e.g., oil, subscript‘o’) on the surface (subscript ‘s’) in the presence of vapor phase(subscript ‘v’, e.g., air).

In another aspect, the invention is directed to a liquid-impregnatedsurface, said surface comprising an impregnating liquid and a matrix ofsolid features spaced sufficiently close to stably contain theimpregnating liquid therebetween or therewithin, wherein one or both ofthe following holds: (i) θ_(os(v),receding)>0; and (ii)θ_(os(w),receding)>0, where θ_(os(v),receding) is receding contact angleof the impregnating liquid (e.g., oil, subscript ‘o’) on the surface(subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g.,air), and where θ_(os(w),receding) is receding contact angle of theimpregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript‘s’) in the presence of water (subscript ‘w’).

In some embodiments, both θ_(os(v),receding)>0 and θ_(os(w),receding)>0.In some embodiments, one or both of the following holds: (i)θ_(os(v),receding)<θ_(c); and (ii) θ_(os(w),receding)<θ_(c), where θ_(c)is critical contact angle. In some embodiments, one or both of thefollowing holds: (i) θ_(os(v),receding)<θ*_(c); and (ii)θ_(os(w),receding)<θ*_(c), where θ*_(c)=cos⁻¹(1/r), and where r isroughness of the solid portion of the surface.

In some embodiments, the article is a member selected from the groupconsisting of a pipeline, a steam turbine part, a gas turbine part, anaircraft part, a wind turbine part, eyeglasses, a mirror, a powertransmission line, a container, a windshield, an engine part, a nozzle,a tube, or a portion or coating thereof.

In another aspect, the invention is directed to an article comprising aninterior surface, said article being at least partially enclosed (e.g.,the article is an oil pipeline, other pipeline, consumer productcontainer, other container) and adapted for containing or transferring afluid of viscosity μ₁, wherein the interior surface comprises aliquid-impregnated surface, said liquid-impregnated surface comprisingan impregnating liquid and a matrix of solid features spacedsufficiently close to stably contain the impregnating liquidtherebetween or therewithin, wherein the impregnating liquid compriseswater (having viscosity μ₂).

In some embodiments, μ₁/μ₂>1. In some embodiments, μ₁/μ₂>0.1. In someembodiments, (h/R)(μ₁/μ₂)>0.1 (where h is average height of the solidfeatures and R is the radius of the pipe or the average fluid depth inan open system). In some embodiments, (h/R)(μ₁/μ₂)>0.5. In someembodiments, R<1 mm.

In some embodiments, the impregnating liquid comprises an additive(e.g., a surfactant) to prevent or reduce evaporation of theimpregnating liquid. In some embodiments, said surface comprises apulled-up region of excess impregnating liquid (e.g., oil) extendingabove said solid features.

In another aspect, the invention is directed to an article comprising aliquid-impregnated surface, said surface comprising an impregnatingliquid and a matrix of solid features spaced sufficiently close tostably contain the impregnating liquid therebetween or therewithin,wherein one or both of the following holds: (i) 0<ϕ≤0.25, where ϕ is arepresentative fraction of the projected surface area of theliquid-impregnated surface corresponding to non-submerged solid (i.e.,non-submerged by the impregnating liquid—can be “non-submerged” andstill in contact with the non-vapor phase external to the surface) atequilibrium (e.g., where equilibrium can encompass pseudo-equilibrium);and (ii) S_(oe(v))<0, where S_(oe(v)) is spreading coefficient, definedas γ_(ev)−γ_(eo)−γ_(ov), where γ is the interfacial tension between thetwo phases designated by subscripts, said subscripts selected from e, v,and o, where e is a non-vapor phase (e.g., liquid or semi-solid)external to the surface and different from the impregnating liquid, v isvapor phase external to the surface (e.g., air), and o is theimpregnating liquid.

In some embodiments, 0<ϕ≤0.25. In some embodiments, 0.01<ϕ≤0.25. In someembodiments, 0.05<ϕ≤0.25. In some embodiments, S_(oe(v))<0.

In some embodiments, the impregnating liquid comprises at least onemember selected from the group consisting of silicone oil, propyleneglycol dicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin(PAO), synthetic hydrocarbon cooligomer, fluorinated polysiloxane,propylene glycol, tetrachloroethylene (perchloroethylene), phenylisothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene,o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene,acetylene tetrabromide, 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl)imide (BMIm), tribromohydrin(1,2,3-tribromopropane), ethylene dibromide, carbon disulfide,bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquidpetrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbondisulfide, phenyl mustard oil, monoiodobenzene,alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butylalcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleicacid, and amyl phthalate.

In some embodiments, the solid features comprise at least one memberselected from the group consisting of a polymeric solid, a ceramicsolid, a fluorinated solid, an intermetallic solid, and a compositesolid. In some embodiments, the solid features comprise a chemicallymodified surface, coated surface, surface with a bonded monolayer. Insome embodiments, the solid features define at least one member selectedfrom the group consisting of pores, cavities, wells, interconnectedpores, and interconnected cavities. In some embodiments, the solidfeatures comprise at least one member selected from the group consistingof posts, nanoneedles, nanograss, substantially spherical particles, andamorphous particles. In some embodiments, the solid features have arough surface (e.g., the solid features have a surface roughness<1 μm).In some embodiments, the rough surface provides stable impregnation ofliquid therebetween or therewithin, such that θ_(os(v),receding)<θ_(c),where θ_(c) is critical contact angle. In some embodiments, theliquid-impregnated surface is configured such that water dropletscontacting the surface are not pinned or impaled on the surface and havea roll-off angle α of less than 40°. In some embodiments, the waterdroplets have a roll-off angle α of less than 35°, less than 30°, lessthan 25°, or less than 20°.

In another aspect, the invention is directed to an article comprising aliquid-impregnated surface, said surface comprising an impregnatingliquid and a matrix of solid features spaced sufficiently close tostably contain the impregnating liquid therebetween or therewithin,wherein one or both of the following holds: (i) θ_(os(e),receding)=0;and (ii) θ_(os(v),receding)=0 and θ_(os(e),receding)=0, whereθ_(os(e),receding) is receding contact angle of the impregnating liquid(e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in thepresence of a non-vapor (e.g., liquid, solid, semi-solid, gel) phaseexternal to the surface that is different from the impregnating liquid(subscript ‘e’), and where θ_(os(v),receding) is receding contact angleof the impregnating liquid (e.g., oil, subscript ‘o’) on the surface(subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g.,air).

In another aspect, the invention is directed to an comprising aliquid-impregnated surface, said surface comprising an impregnatingliquid and a matrix of solid features spaced sufficiently close tostably contain the impregnating liquid therebetween or therewithin,wherein one or both of the following holds: (i) θ_(os(v),receding)>0;and (ii) θ_(os(e),receding)>0, where θ_(os(v),receding) is recedingcontact angle of the impregnating liquid (e.g., oil, subscript ‘o’) onthe surface (subscript ‘s’) in the presence of vapor phase (subscript‘v’, e.g., air), and where θ_(os(e),receding) is receding contact angleof the impregnating liquid (e.g., oil, subscript ‘o’) on the surface(subscript ‘s’) in the presence of a non-vapor (e.g., liquid, solid,semi-solid, gel) phase external to the surface that is different fromthe impregnating liquid (subscript ‘e’).

In some embodiments, both θ_(os(v),receding)>0 and θ_(os(e),receding)>0.In some embodiments, one or both of the following holds: (i)θ_(os(v),receding)<θ_(c); and (ii) θ_(os(e),receding)<θ_(c), where θ_(c)is critical contact angle. In some embodiments, one or both of thefollowing holds: (i) θ_(os(v),receding)<θ*_(c); and (ii)θ_(os(e),receding)<θ_(c), where θ*_(c)=cos⁻¹(1/r), and where r isroughness of the solid portion of the surface.

In some embodiments, the article is a member selected from the groupconsisting of a pipeline, a steam turbine part, a gas turbine part, anaircraft part, a wind turbine part, eyeglasses, a mirror, a powertransmission line, a container, a windshield, an engine part, tube,nozzle, or a portion or coating thereof. In some embodiments, saidsurface comprises a pulled-up region of excess impregnating liquid(e.g., oil) extending above said solid features.

In some embodiments of any of the aspects described herein (e.g., hereinabove), the article further comprises material of said non-vapor phaseexternal to said surface (and in contact with said surface), saidarticle containing said non-vapor phase material [e.g. wherein thearticle is a container, a pipeline, nozzle, valve, a conduit, a vessel,a bottle, a mold, a die, a chute, a bowl, a tub, a bin, a cap (e.g.,laundry detergent cap), and/or a tube]. In some embodiments, saidmaterial of said non-vapor phase external to said surface comprises oneor more of the following: food, cosmetic, cement, asphalt, tar, icecream, egg yolk, water, alcohol, mercury, gallium, refrigerant,toothpaste, paint, peanut butter, jelly, jam, mayonnaise, ketchup,mustard, condiment, laundry detergent, consumer product, gasoline,petroleum product, oil, biological fluid, blood, plasma.

In another aspect, the invention is directed to a method of using anyarticle described herein (e.g., herein above), the method comprising thestep of exposing said surface to water.

In another aspect, the invention is directed to a method of using thearticle of any one of claims 1 to 10, the method comprising the step ofexposing said surface to said non-vapor phase (e.g., liquid orsemi-solid) external to the surface and different from the impregnatingliquid. In some embodiments, the non-vapor phase comprises one or moreof the following: food, cosmetic, cement, asphalt, tar, ice cream, eggyolk, water, alcohol, mercury, gallium, refrigerant, toothpaste, paint,peanut butter, jelly, jam, mayonnaise, ketchup, mustard, condiment,laundry detergent, consumer product, gasoline, petroleum product, oil,biological fluid, blood, plasma.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the invention can be better understood withreference to the drawing described below, and the claims.

FIG. 1 illustrates a schematic cross-sectional and corresponding topview of a liquid-impregnated surface that are partially submerged.

FIG. 1(a) illustrates a schematic diagram of a liquid droplet placed ona textured surface impregnated with a lubricant that wets the solidcompletely.

FIG. 1(b) illustrates a schematic diagram of a liquid droplet placed ona textured surface impregnated with a lubricant that wets the solid witha non-zero contact angle in the presence of air and the droplet liquid.

FIG. 1(c) illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with silicone oil.

FIG. 1(d) illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm).

FIGS. 1(e) and 1(f) illustrate a water droplet under UV illuminationwhen a fluorescent dye was dissolved in silicone oil and BMIm. Thebottom regions show that the lubricating oils are pulled up above thetexture surface (b=50 μm).

FIGS. 1(g) and 1(h) show laser confocal fluorescence microscopy (LCFM)images of the impregnated texture showing that post tops were bright inthe case of silicone oil (FIG. 1(g)), suggesting that they were coveredwith oil, and were dark in the case of BMIm (FIG. 1(h)), suggesting thatthey were dry.

FIG. 1(i) illustrates an ESEM image of the impregnated texture showingthe silicone oil trapped in the texture and suggesting that the filmthat wets the post tops is thin.

FIG. 1(j) illustrates a SEM image of the texture impregnated with BMImshowing discrete droplets on post tops indicating that a film was notstable in this case.

FIG. 1(k) illustrates schematics of wetting configurations outside andunderneath a drop. The total interface energies per unit area arecalculated for each configuration by summing the individual interfacialenergy contributions. Equivalent requirements for stability of eachconfiguration are also shown in FIG. 1(a).

FIG. 2 illustrates a schematic diagram of possible thermodynamic statesof a water droplet placed on a lubricant-encapsulated surface. The toptwo schematics illustrate whether or not the droplet becomes cloaked bythe lubricant. For each case, there are six possible states, asillustrated, depending on how the lubricant wets the texture in thepresence of air (the vertical axis) and water (horizontal axis).

FIG. 3(a) illustrates measured velocities of water droplets as afunction of substrate tilt angle for various lubricant viscosities, postspacings, and droplet sizes.

FIG. 3(b) is a schematic of a water droplet moving on alubricant-impregnated surface showing the various parameters consideredin the scaling model.

FIG. 3(c) illustrates trajectories of a number of coffee particlesmeasured relative to the water droplet revealing that the drop rollsrather than slips across the surface.

FIG. 3(d) is a non-dimensional plot that collapses the data points shownin FIG. 3(a) onto a single curve.

FIG. 4 is a schematic describing six liquid-impregnated surface wettingstates, in accordance with certain embodiments of the invention.

FIG. 5 is a schematic showing conditions for the six liquid-impregnatedsurface wetting states shown in FIG. 4 in accordance with certainembodiments of the invention.

FIG. 6 includes a plot of roll-off angle versus emerged area fraction ϕand two SEM images of BMIm impregnated texture, in accordance withcertain embodiments of the invention.

FIGS. 7 and 8 demonstrate condensation inhibition by preventingcoalescence due to liquid cloaking, in accordance with certainembodiments of the invention.

FIG. 9 demonstrates condensation inhibition by the decreased drainagerate of oil between neighboring water droplets, particularly where theoil has high viscosity, in accordance with certain embodiments of theinvention.

FIG. 10 demonstrates frost inhibition because of decreased drainage rateof oil between neighboring water droplets, particularly where the oilhas high viscosity, in accordance with certain embodiments of theinvention.

FIG. 11(a) shows measured roll-off angles for different encapsulatingliquids as a function of post spacing b, according to some embodimentsdescribed herein. Extremely low roll-off angles were observed in someembodiments in the case of silicone oil impregnated surfaces, consistentwith the post tops being encapsulated both outside and underneath thedroplet (state A3-W3, θ_(os(a)), θ_(os,w)=0). The high roll-off anglesseen in the case of BMIm impregnated surfaces are consistent with thepost tops being emergent outside and underneath the droplet (stateA2-W2, θ_(c)>θ_(os(a)), θ_(os(w))>0).

FIG. 11(b) shows an SEM image of the BMIm impregnated texture andreveals that the post tops are dry, in accordance with certainembodiments of the invention.

FIG. 11(c) shows an SEM image of the posts that are further roughened byadding nanograss, the posts are covered with BMIm and consequently, theroll-off angle decreases, in accordance with certain embodiments of theinvention.

FIG. 11(d) shows a non-dimensional plot of scaled gravitational force(left side of Eq. (11) discussed below) at the instant of roll-off as afunction of the relevant pinning force (right side of Eq. (11) discussedbelow), demonstrating that the roll-off data is in general agreementwith the scaling, in accordance with certain embodiments of theinvention.

FIG. 12(a) is a SEM image of a silicon micropost array, in accordancewith certain embodiments of the invention.

FIG. 12(b) is a SEM image of silicon microposts etched with nanograss,in accordance with certain embodiments of the invention.

FIG. 13 shows SEM images of nanograss-covered silicon micropillarsimpregnated with an ionic liquid (BMIm), in accordance with certainembodiments of the invention. In some embodiments, BMIm completely fillsthe voids between the nano-ridges, as shown on the right, resulting inalmost no exposure of the solid surface to air after dip-coating (ϕ≅0).

DESCRIPTION

It is contemplated that compositions, mixtures, systems, devices,methods, and processes of the claimed invention encompass variations andadaptations developed using information from the embodiments describedherein. Adaptation and/or modification of the compositions, mixtures,systems, devices, methods, and processes described herein may beperformed by those of ordinary skill in the relevant art.

Throughout the description, where articles, devices, apparatus andsystems are described as having, including, or comprising specificcomponents, or where processes and methods are described as having,including, or comprising specific steps, it is contemplated that,additionally, there are articles, devices, apparatus and systems of thepresent invention that consist essentially of, or consist of, therecited components, and that there are processes and methods accordingto the present invention that consist essentially of, or consist of, therecited processing steps.

Similarly, where articles, devices, mixtures, apparatus and compositionsare described as having, including, or comprising specific compoundsand/or materials, it is contemplated that, additionally, there arearticles, devices, mixtures, apparatus and compositions of the presentinvention that consist essentially of, or consist of, the recitedcompounds and/or materials.

It should be understood that the order of steps or order for performingcertain actions is immaterial so long as the invention remains operable.Moreover, two or more steps or actions may be conducted simultaneously.

The mention herein of any publication, for example, in the Backgroundsection, is not an admission that the publication serves as prior artwith respect to any of the claims presented herein. The Backgroundsection is presented for purposes of clarity and is not meant as adescription of prior art with respect to any claim.

Surfaces with designed chemistry and roughness possess remarkablenon-wetting properties, which can be very useful in a wide variety ofcommercial and technological applications, as will be described infurther detail below.

In some embodiments, where “a” is used as a subscript of a variable todenote air, “v” is also appropriate (where v indicates a vapor phase).Also, where “w” as a subscript of a variable to denote water, “e” isalso appropriate (where e indicates a non-vapor (e.g., liquid, solid,semi-solid, gel) phase external to the surface that is different fromthe impregnating liquid.

In some embodiments, a non-wetting, liquid-impregnated surface isprovided that includes a solid having textures (e.g., posts) that areimpregnated with an impregnating liquid. In some embodiments, thelubricant is stabilized by the capillary forces arising from themicroscopic texture, and provided that the lubricant wets the solidpreferentially, this allows the droplet to move (e.g., slide, roll,slip, etc.) above the liquid-impregnated surface with remarkable ease,as evidenced by the extremely low contact angle hysteresis (˜1°) of thedroplet. In some embodiments, in addition to low hysteresis, thesenon-wetting surfaces can provide self-cleaning properties, withstandhigh drop impact pressures, self-heal by capillary wicking upon damage,repel a variety of liquids, and reduce ice adhesion. Contact linemorphology governs droplet pinning and hence its mobility on thesurface.

In general, solid features can be made from or can comprise any materialsuitable for use in accordance with the present invention. In accordancewith various embodiments of the present invention, micro-scale solidfeatures are used (e.g., from about 1 micron to about 100 microns incharacteristic dimension, e.g., from about 1-10 microns, 10-20 microns,20-30 microns, 30-50 microns, 50-70 microns, 70-100 microns). In certainembodiments, nano-scale solid features are used (e.g., less than about 1micron, e.g., about 1 nm to about 1 micron e.g., about 1-10 nm, 10-50nm, 50-100 nm, 100-200 nm, 200-300 nm, 300-500 nm, 500-700 nm, 700 nm-1micron).

In some embodiments, micro-scale features are used. In some embodiments,a micro-scale feature is a particle. Particles can be randomly oruniformly dispersed on a surface. Characteristic spacing betweenparticles can be about 200 μm, about 100 μm, about 90 μm, about 80 μm,about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about20 μm, about 10 μm, about 5 μm or 1 μm. In some embodiments,characteristic spacing between particles is in a range of 100 μm-1 μm,50 μm-20 μm, or 40 μm-30 μm. In some embodiments, characteristic spacingbetween particles is in a range of 100 μm-80 μm, 80 μm-50 μm, 50 μm-30μm or 30 μm-10 μm. In some embodiments, characteristic spacing betweenparticles is in a range of any two values above.

Particles can have an average dimension of about 200 μm, about 100 μm,about 90 μm, about 80, about 70 μm, about 60 μm, about 50 μm, about 40μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm or 1 μm. In someembodiments, an average dimension of particles is in a range of 100 μm-1μm, 50 μm-10 μm, or 30 μm-20 μm. In some embodiments, an averagedimension of particles is in a range of 100 μm-80 μm, 80 μm-50 μm, 50μm-30 μm or 30 μm-10 μm. In some embodiments, an average dimension ofparticles is in a range of any two values above.

In some embodiments, particles are porous. Characteristic pore size(e.g., pore widths or lengths) of particles can be about 5000 nm, about3000 nm, about 2000 nm, about 1000 nm, about 500 nm, about 400 nm, about300 nm, about 200 nm, about 100 nm, about 80 nm, about 50, about 10 nm.In some embodiments, characteristic pore size is in a range of 200 nm-2μm or 100 nm-1 μm. In some embodiments, characteristic pore size is in arange of any two values above.

In some embodiments, the liquid-impregnated surface is configured suchthat water droplets contacting the surface are not pinned or impaled onthe surface.

As used herein, emerged area fraction ϕ is defined as a representativefraction of the projected surface area of the liquid-impregnated surfacecorresponding to non-submerged solid at equilibrium. The term“equilibrium” as used herein refers to the condition in which theaverage thickness of the impregnating film does not change over time dueto drainage by gravity when the substrate is held away from horizontal,and where evaporation is negligible (e.g., if the liquid impregnatedliquid were to be placed in an environment saturated with the vapor ofthat impregnated liquid). Similarly, the term “pseudo-equilibrium” asused herein refers to equilibrium with the condition that evaporationmay occur or gradual dissolving may occur. Note that the averagethickness of a film at equilibrium may be less on parts of the substratethat are at a higher elevation, due to the decreased hydrostaticpressure within the film at increasing elevation. However, it willeventually reach an equilibrium (or pseudo-equilibrium), in which theaverage thickness of any part of the surfaces is unchanging with time.

In general, a “representative fraction” of a surface refers to a portionof the surface with a sufficient number of solid features thereupon suchthat the portion is reasonably representative of the whole surface. Incertain embodiments, a “representative fraction” is at least a tenth ofthe whole surface.

Referring to FIG. 1, a schematic cross-sectional view and thecorresponding top view of a liquid-impregnated surface that is partiallysubmerged is shown. The upper left drawing of FIG. 1 shows across-sectional view of a row of cone-shaped solid features. Theprojected surface area of the non-submerged solid 102 is illustrated asshaded areas of the overhead view, while the remaining non-shaded arearepresents the projected surface area of the submergedliquid-impregnated surface 100. In addition to the projection surfacearea of this row of solid features, other solid features placed in asemi-random pattern are shown in shade in the overhead view. Similarly,the cross-section view of a row of evenly spaced posts is shown on theright of FIG. 1. Additional rows of well-patterned posts are shown inshade in the overhead view. As demonstrated, in some embodiments of thepresent invention, a liquid-impregnated surface includes randomly and/ornon-randomly patterned solid features.

In certain embodiments of the present invention, ϕ is less than 0.30,0.25, 0.20, 0.15, 0.10, 0.05, 0.01, or 0.005. In certain embodiments, ϕis greater than 0.001, 0.005, 0.01, 0.05, 0.10, 0.15, or 0.20. Incertain embodiments, ϕ is in a range of about 0 and about 0.25. Incertain embodiments, ϕ is in a range of about 0 and about 0.01. Incertain embodiments, ϕ is in a range of about 0.001 and about 0.25. Incertain embodiments, ϕ is in a range of about 0.001 and about 0.10.

In some embodiments, the liquid-impregnated surface is configured suchthat cloaking by the impregnating liquid can be either eliminated orinduced, according to different embodiments described herein.

As used herein, the spreading coefficient, S_(ow(a)), is defined asγ_(wa)−γ_(wo)−γ_(oa), where γ is the interfacial tension between the twophases designated by subscripts w, a, and o, where w is water, a is air,and o is the impregnating liquid. Interfacial tension can be measuredusing a pendant drop method as described in Stauffer, C. E., “Themeasurement of surface tension by the pendant drop technique,” J. Phys.Chem. 1965, 69, 1933-1938, the text of which is incorporated byreference herein. Exemplary surfaces and its interfacial tensionmeasurements (at approximately 25° C.) are Table 3 below.

Without wishing to be bound to any particular theory, impregnatingliquids that have S_(ow(a)), less than 0 will not cloak matter as seenin FIG. 1(c), resulting in no loss of impregnating liquids, whereasimpregnating liquids that have S_(ow(a)) greater than 0 will cloakmatter (condensed water droplets, bacterial colonies, solid surface) asseen in FIG. 1(b) and this may be exploited to prevent corrosion,fouling, etc. In certain embodiments, cloaking is used for preventingvapor-liquid transformation (e.g., water vapor, metallic vapor, etc.).In certain embodiments, cloaking is used for inhibiting liquid-solidformation (e.g., ice, metal, etc.). In certain embodiments, cloaking isused to make reservoirs for carrying the materials, such thatindependent cloaked materials can be controlled and directed by externalmeans (like electric or magnetic fields).

FIG. 1(c) illustrates a water droplet on a silicon micro post surface(post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with silicone oil. FIG. 1(d)illustrates a water droplet on a silicon micro post surface (post sidea=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS(octadecyltrichlorosilane) and impregnated with1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm).FIGS. 1(e) and 1(f) illustrate a water droplet under UV illuminationwhen a fluorescent dye was dissolved in silicone oil and BMIm. Thebottom regions show that the lubricating oils are pulled up above thetexture surface (b=50 μm).

FIG. 1(c) shows an 8 μl water droplet placed on the silicone oilimpregnated texture. The droplet forms a large apparent contact angle(˜100°) but very close to the solid surface (shown by arrows in FIG.1(c)), its profile changes from convex to concave.

When a fluorescent dye was added to the silicone oil and imaged under UVlight, the point of inflection corresponded to the height to which anannular ridge of oil was pulled up in order to satisfy a vertical forcebalance of the interfacial tensions at the inflection point (FIG. 1(e)).Although the oil should spread over the entire droplet (FIG. 1(c)), thecloaking film was too thin to be captured in these images. The “wettingridge” was also observed in the case of ionic liquid (FIGS. 1(d), 1(f)).The importance of the wetting ridge to droplet mobility will bediscussed below. Such wetting ridges are reminiscent of those observedaround droplets on soft substrates.

The texture can be completely submerged in the oil if θ_(os(a))=0°. Thiscondition was found to be true for silicone oil, implying that the topsof the posts should be covered by a stable thin oil film. This film wasobserved experimentally using laser confocal fluorescence microscopy(LCFM); the post tops appear bright due to the presence of a fluorescentdye that was dissolved in the oil (FIG. 1(g)). Environmental SEM imagesof the surface (FIG. 1(i)) show the oil-filled texture and confirm thatthis film is less than a few microns thick, consistent with priorestimates of completely-wetting films. On the other hand, BMIm has anon-zero contact angle on a smooth OTS-coated silicon surface(θ_(os(a))=65±5°) indicating that with this lubricant the post topsshould remain dry. Indeed, LCFM images confirmed this (FIG. 1 (h))—thepost tops appear dark as there is no dye present to fluoresce. SinceBMIm is conductive and has an extremely low vapor pressure, it could beimaged in a SEM. As shown in FIG. 1(j), discrete droplets resting onpost tops are seen, confirming that a thin film was not stable on thepost tops in this case.

The stable wetting configuration affects the mobility of droplets. Asshown in FIG. 1(b), in the case of BMIm, there are three distinct phasecontact lines at the perimeter of the drop that confine the wettingridge: the oil-water-air contact line, the oil-solid-air contact lineoutside the drop, and the oil-solid-water contact line underneath thedrop. These contact lines exist because θ*_(os(a))>θ, _(θos(w))>0, andS_(ow(a))<0. In contrast, in the case of silicone oil (FIG. 1(a)), noneof these contact lines exist because θ_(os(a))=0, θ_(os(w))=0, andS_(ow(a))>0. These configurations are just two of the 12 differentconfigurations in such a four-phase system where oil impregnation ispossible. These configurations are discussed below.

A thermodynamic framework that allows one to predict which of these 12states will be stable for a given droplet, oil, and substrate materialwill be discussed in the paragraphs below. There are three possibleconfigurations to consider for the interface outside of the droplet (inan air environment), and three possible configurations to consider forthe interface underneath the droplet (in a water environment). Theseconfigurations are shown in FIG. 1(k) along with the total interfaceenergy of each configuration. The configurations possible outside thedroplet are A1 (not impregnated, i.e., dry), A2 (impregnated withemergent features), and A3 (impregnated with submerged features—i.e.,encapsulated). On the other hand, underneath the droplet, the possibleconfigurations are W1 (impaled), W2 (impregnated with emergentfeatures), and W3 (impregnated with submerged features—i.e.,encapsulated). The stable configuration will be the one that has thelowest total interface energy. Referring now to configurations outsidethe droplet, the textured surface as it is slowly withdrawn from areservoir of oil could be in any of states A1, A2, and A3 depending onwhich has the lowest energy. For example, state A2 would be stable if ithas the lowest total interface energy, i.e. E_(A2)<E_(A1), E_(A3). FromFIG. 1(k), this results in:E _(A2) <E _(A1)

(γ_(sa)−γ_(os))/γ_(oa)>(1−ϕ)/(r−ϕ)  (1)E _(A2) <E _(A3)

γ_(sa)−γ_(os)−γ_(oa)<0  (2)

where ϕ is the fraction of the projected area of the surface that isoccupied by the solid and r is the ratio of total surface area to theprojected area of the solid. In the case of square posts with width “a”,edge-to-edge spacing “b”, and height “h”, ϕ=a²/(a+b)² andr=1+4ah/(a+b)². Applying Young's equation,cos(θos(a))=(γ_(sa)−γ_(os))/γ_(oa), Eq. (1) reduces to the hemi-wickingcriterion for the propagation of oil through a textured surface:cos(θ_(os(a)))>(1−ϕ)/(r−ϕ)=cos(θ_(c)). This requirement can beconveniently expressed as θ_(os(a))<θ_(c). In Eq. (2),γ_(sa)−γ_(os)−γ_(oa), is simply the spreading coefficient S_(os(a)) ofoil on the textured surface in the presence of air. This may bereorganized as (γ_(sa)−γ_(os))/γ_(oa)<1, and applying Young's equationagain, Eq. (2) can be written as θ_(os(a))>0. Expressing Eq. (1) interms of the spreading coefficient S_(os(a)), yields:−γ_(oa)(r−1)/(r−ϕ)<S_(os(a)). The above simplifications then lead to thefollowing equivalent criteria for the surface to be in state A2:E _(A2) <E _(A1) ,E _(A3)

θ_(c)>θ_(os(a))>0

γ_(oa)(r−1)/(r−ϕ)<S _(os(a))<0  (3)

Similarly, state A3 would be stable if E_(A3)<E_(A2), E_(A1). From FIG.1(k), this gives:E _(A3) <E _(A2)

θ_(os(a))=0

γ_(sa)−γ_(oa) ≡S _(os(a))≥0  (4)E _(A3) <E _(A1)

θ_(os(a))<cos⁻¹(1/r)

S _(os(a))>−γ_(oa)(1/1/r)  (5)

Note that Eq. (5) is automatically satisfied by Eq. (4), thus thecriterion for state A3 to be stable (i.e., encapsulation) is given byEq. (4). Following a similar procedure, the condition for state A1 to bestable can be derived asE _(A1) <E _(A2) ,E _(A3)

θ_(os(a))>θ_(c)

S _(os(a))<−γ_(oa)(r−1)/(r−ϕ)  (6)

The rightmost expression of Eq. (4) can be rewritten as(γ_(sa)−γ_(os))/γ_(oa)≥1. This raises an important point: Young'sequation would suggest that if θ_(os(a))=0, then(γ_(sa)−γ_(os))/γ_(oa)=1 (i.e., S_(os(a))=0). However, θ_(os(a))=0 istrue also for the case that (γ_(sa)−γ_(os))/γ_(oa)>1 (i.e. S_(os(a))>0).It is important to realize that Young's equation predicts the contactangle based on balancing the surface tension forces on a contactline—the equality only exists for a contact line at static equilibrium.For a spreading film (S_(os(a))>0) a static contact line doesn't exist,hence precluding the applicability of Young's equation.

The configurations possible underneath the droplet are discussed in theparagraphs below. Upon contact with water, the interface beneath thedroplet will attain one of the three different states—W1, W2, or W3(FIG. 1(k))—depending on which has the lowest energy. Applying the samemethod to determine the stable configurations of the interface beneaththe droplet, and using the total interface energies provided in Table 1,the stability requirements take a form similar to Eqs. (3), (4), and(6), with γ_(oa), γ_(sa), θ_(os(a)), S_(os(a)), replaced with γ_(ow),γ_(sw), θ_(os(w)), S_(os(w)) respectively. Notice also that θ_(c) is notaffected by the surrounding environment as it is only a function of thetexture parameters, ϕ and r. Thus, the texture will remain impregnatedwith oil beneath the droplet with emergent post tops (i.e., state W2)when:E _(W2) <E _(W1) ,E _(W3)

θ_(c)>θ_(os(w))>0

−γ_(ow)(r−1)/(r−ϕ)<S _(os(w))<0  (7)State W3 will be stable (i.e., the oil will encapsulate the texture)when:E_(W3)<E_(W1),E_(W2)

θ_(os(w))=0

γ_(sw)−γ_(os)−γ_(ow) −S _(os(w))≥0  (8)and the droplet will displace the oil and be impaled by the textures(state W1) when:E _(W1) <E _(W2) ,E _(W3)

θ_(os(w))>θ_(c)

S _(os(w))<−γ_(ow)(r−1)/(r−ϕ)  (9)

Combining the above criteria along with the criterion for cloaking ofthe water droplet by the oil film described earlier, the variouspossible states can be organized in a regime map, which is shown FIG. 3.The cloaking criterion is represented by the upper two schematicdrawings. For each of these cases, there are six differentconfigurations possible depending on how the oil interacts with thesurface texture in the presence of air (vertical axis in FIG. 3) andwater (horizontal axis in FIG. 3). The vertical and horizontal axes arethe normalized spreading coefficients S_(os(a))/γ_(oa) andS_(os(w))/γ_(ow) respectively. Considering first the vertical axis ofFIG. 3, when S_(os(a))/γ_(oa)<−(r−1)/(r−ϕ), i.e., when Eq. (6) holds,oil does not even impregnate the texture. As S_(os(a))/γ_(oa) increasesabove this important value, impregnation becomes feasible but the posttops are still left emerged. Once S_(os(a))/γ_(oa)>0, the post tops arealso submerged in the oil leading to complete encapsulation of thetexture. Similarly, on the x-axis of FIG. 3 moving from left to right,as S_(os(w))/γ_(ow) increases, the droplet transitions from an impaledstate to an impregnated state to a fully-encapsulated state. Althoughprior studies have proposed simple criteria for whether a deposited dropwould float or sink, additional states, as shown in FIG. 3, were notrecognized.

FIG. 3 shows that there can be up to three different contact lines, twoof which can get pinned on the texture. The degree of pinning determinesthe roll-off angle α*, the angle of inclination at which a dropletplaced on the textured solid begins to move. Droplets that completelydisplace the oil (states A3-W1, A2-W1 in FIG. 3) are not expected toroll off the surface. These states are achieved when θ_(ow)>θ_(c), as isthe case for both BMIm and silicone oil impregnated surfaces when thesilicon substrates are not treated with OTS. As expected, droplets didnot roll off of these surfaces. Droplets in states with emergent posttops (A3-W2, A2-W2, A2-W3) are expected to have reduced mobility that isstrongly texture dependent, whereas those in states with encapsulatedposts outside and beneath the droplet (the A3-W3 states in FIG. 3) areexpected to exhibit no pinning and consequently infinitesimally smallroll-off angles.

Roll-off angles of 5 μl droplets on silicone oil and BMIm impregnatedtextures while varying the post spacing b were measured experimentally.For comparison, the same textures without a lubricant (i.e., theconventional superhydrophobic case) were also evaluated. The results ofthese experiments are shown in FIG. 11(a). The silicone oil encapsulatedsurfaces have extremely low roll-off angles regardless of the postspacing and oil viscosity, showing that contact line pinning wasnegligible, as predicted for a liquid droplet in an A3-W3 state with nocontact lines on the textured substrate. On the other hand, BMImimpregnated textures showed much higher roll-off angles, which increasedas the spacing decreased—a trend that is similar to Cassie droplets onsuperhydrophobic surfaces. This observation illustrates that pinning wassignificant in this case, and occurs on the emergent post tops,illustrated in FIG. 11(b). However, the pinning was significantlyreduced by adding a second smaller length scale texture (i.e., nanograsson the posts), so that BMIm impregnated the texture even on the posttops, thereby substantially reducing ϕ (as illustrated by FIG. 1 (c) aswell as FIGS. 12-13). The roll-off angle decreased from over 30° to onlyabout 2°. The reduction in the emergent area fraction ϕ was not due tothe absolute size of the texture features; since the oil-water andoil-air interfaces must intersect surface features at contact anglesθ_(os(w)) and θ_(ow(a)), ϕ rather depends on these contact angles andfeature geometry.

The effect of texture on the roll-off angle can be modelled by balancinggravitational forces with pinning forces. A force balance of a waterdroplet on a smooth solid surface at incipient motion gives ρ_(w)Ωg sinα*≈2R_(b)γ_(wa) (cos θ_(rec,ws(a))−cos θ_(adv,ws(a))), where ρ_(w) isthe density of the liquid droplet of volume Ω, g is the gravitationalacceleration, R_(b) is the droplet base radius, and θ_(adv,ws(a)) andθ_(rec,ws(a)) are the advancing and receding contact angles of dropletin air on the smooth solid surface. To extend this treatment to oursystem, we recognize that pinning results from contact angle hysteresisof up to two contact lines: an oil-air-solid contact line with a pinningforce per unit length given by γ_(oa)(cos θ_(rec,os(a))−cosθ_(adv,os(a))) and an oil-water-solid contact line with a pinning forceper unit length given by γ_(ow)(cos θ_(rec,os(w))−cos θ_(adv,os(w))). Insome embodiments, the length of the contact line over which pinningoccurs is expected to scale as R_(b)ϕ^(1/2), where ϕ^(1/2) is thefraction of the droplet perimeter (˜R_(b)) making contact with theemergent features of the textured substrate. Thus, a force balancetangential to the surface gives:ρ_(w) Ωg sin α*˜R _(b)ϕ^(1/2)[γ_(ow)(cos θ_(rec,os(w))−cosθ_(adv,os(w)))+γ_(oa) cos θ_(rec,os(a))−cos θ_(adv,os(a)))]   (10)Dividing Eq. (10) by R_(b)γ_(wa), we obtain a non-dimensionalexpression:Bo sin α*f(θ)˜ϕ_(1/2)[γ_(ow)(cos θ_(rec,os(w))−cosθ_(adv,os(w)))+γ_(oa)(cos θ_(rec,os(a))−cos θ_(adv,os(a)))]/γ_(wa)  (11)where

$\left. {{f(\theta)} = {\frac{\Omega^{\frac{1}{3}}}{R_{b}} = \left\lbrack {\left( \frac{\pi}{3} \right)\left( {2 + {\cos\;\theta}} \right){\left( {1 - {\cos\;\theta}} \right)^{2}/\sin^{3}}\theta} \right)}} \right\rbrack^{1/3}$by assuming the droplet to be a spherical cap making an apparent contactangle θ with the surface.

${Bo} = {\Omega^{\frac{2}{3}}\rho_{w}{g/\gamma_{wa}}}$is the Bond number, which compares the relative magnitude ofgravitational forces to surface tension forces. Values forθ_(rec,os(w)), θ_(adv,os(w)), θ_(rec,os(a)), θ_(adv,os(a)), γ_(ow),γ_(oa), and γ_(wa) are provided in Tables 2 and 3 below. FIG. 11(d)shows that the measured data is in agreement with the scaling of Eq.(11). The data for the silicone oil encapsulated surface and for theBMIm impregnated, nanograss-covered posts lie close to the origin asboth ϕ and α* are very small in these cases.

Described in the following paragraphs are embodiments that illustratedynamics of droplet shedding. Once the gravitational forces on a dropletovercome the pinning forces, the velocity attained by the dropletdetermines how quickly it can be shed, which reflects the non-wettingperformance of the surface. For a droplet of volume Ω this velocity maydepend on both the contact line pinning and viscosity of the lubricant.In some embodiments, the steady-state shedding velocity V of waterdroplets may be measured using a high-speed camera while systematicallyvarying lubricant dynamic viscosity μ_(o), post spacing b, substratetilt angle α, and droplet volume, Ω. These measurements are illustratedin FIG. 3(a) where V is plotted as a function of a for different μ_(o),b, and Ω; the velocity V, increases with α and Ω as both increase thegravitational force acting on the droplet. However, V decreases withμ_(o) and ϕ as both increase the resistance to droplet motion.

To explain these trends, it must first be determined whether the dropletis rolling or sliding. Referring now to the oil-water interface beneaththe droplet as shown in FIG. 3(b), the shear stress at this interface,on the water side, scales as τ_(w)˜μ_(w)(V−V_(i))/h_(cm), and on the oilside scales as τ_(o)˜μ_(o)V_(i)/t, where V_(i) is the velocity of theoil-water interface and h_(cm) is the height of the centre of mass ofthe droplet above the solid surface, and t is the thickness of the oilfilm. Since τ_(w) must be equal to τ_(o) at the oil-water interface,μ_(w)(V−V_(i))/h_(cm)˜μ_(o)V_(i)/t. Rearranging this yields:V _(i) /V˜(1+(μ_(o) h _(cm))/(μ_(w) t))⁻¹  (12)

Since (μ_(o)/μ_(w))(h_(cm)/t)>>1 in some of the conducted experiments,V_(i)/V<<1, i.e., the oil-water interface moves at a negligibly smallvelocity relative to that of the droplet's center of mass. Thus, in someembodiments, the droplets being shed were rolling off the surface. Theexperiment was repeated with ground coffee particles being added to thewater droplets, and the motion of the ground coffee particles wastracked with a high speed camera as the droplet moved across thesurface. Particle trajectories, shown in FIG. 3(c), clearly show thatthe droplets roll across the liquid-impregnated surface as they are shed(μ_(o)=96.4 cP).

To determine the magnitude of V, the rate of change of gravitationalpotential energy as the droplet rolls down the incline with the totalrate of energy dissipation due to contact line pining and viscouseffects were balanced. The resulting energy balance gives:V(F _(g) −F _(p))˜μ_(w)∫_(Ω) _(drop) ( Vū)_(drop) ² dΩ+μ _(o)∫_(Ω)_(film) ( Vū)_(film) ² dΩ+μoμw∫ _(Ω) _(ridge) ( Vū)_(ridge) ² dΩ.   (13)where F_(g) and F_(p) represent the net gravitational and pinning forcesacting on the droplet, the Ω terms are the volume over which viscousdissipation occurs, and the Vū terms are the corresponding velocitygradients. The form of Eq. (13) is similar to that for viscous dropletsrolling on completely non-wetting surfaces, though additional terms arepresent due to the presence of impregnated oil. The three terms on theright side of Eq.(13) represent the rate of viscous dissipation withinthe droplet (I), in the oil film beneath the droplet (II), and in thewetting ridge near the three-phase contact line (III).

The rate of viscous dissipation within the droplet (I) is primarilyconfined to the volume beneath its centre of mass and can beapproximated as I˜μ_(w)(V/h_(cm))²R_(b) ²h_(cm), where R_(b) is the baseradius of the droplet. Applying geometrical relations for a sphericalcap, R_(b)/h_(cm)=g(θ)=4/3(sin θ)(2+cos θ)/(1+cos θ)², yields:I˜μ_(W)V²R_(b)g(θ)

In some embodiments, the rate of viscous dissipation within the film(II) can be approximated as II˜μ₀(V_(i)/t)²R_(b) ²t. Since(μ_(w)/μ₀)(t/h_(cm))<<1, from Eq.(12),Vū_(film)˜V_(i)/t˜(μ_(w)/μ₀)(V/h_(cm)). Using

${h_{cm} = {R_{b}/{g(\theta)}}},{{{yields}\text{:}\mspace{14mu}{II}} \sim {\frac{\mu_{w}^{2}}{\mu_{0}}{V^{2}\left\lbrack {g(\theta)} \right\rbrack}^{2}t}}$

In some embodiments, the rate of viscous dissipation in the wettingridge (III) can be approximated as III˜μ₀(V/h_(ridge))²R_(b)h_(ridge) ²since fluid velocities within the wetting ridge must scale as thevelocities within the wetting ridge must scale as the velocity of thecentre of mass and vanish at the solid surface, giving velocitygradients that scale as Vū_(ridge)˜V/h_(ridge), where h_(ridge) is theheight of the wetting ridge. Thus, III˜μ₀V²R_(b).

Noting that F_(g)=μ_(w)Ωg sin α and F_(p)=μ_(w)Ωg sin α* and dividingboth sides of Eq.(13) by R_(b)Vγ_(wa) yields.

$\begin{matrix}{{{{Bo}\left( {{\sin\;\alpha} - {\sin\;\alpha^{*}}} \right)}{f(\theta)}} \sim {{Ca}\left\{ {{g(\theta)} + {\left\lbrack {g(\theta)} \right\rbrack^{2}\frac{\mu_{w}}{\mu_{0}}\frac{t}{R_{b}}} + \frac{\mu_{0}}{\mu_{w}}} \right\}}} & (14)\end{matrix}$where Ca=μ_(w)V/γ_(wa), is the capillary number, Bo=Ω^(2/3)μ_(w)g/γ_(wa) is the Bond number, and f(θ)=Ω^(1/3)/R_(b). Since(μ_(w)/μ₀)(t/R_(b))<<1, and μ₀/μ_(w)>>g(θ) in some embodiments andexperiments, Eq. (14) can be simplified to:

$\begin{matrix}{{{{Bo}\left( {{\sin\;\alpha} - {\sin\;\alpha^{*}}} \right)}{f(\theta)}} \sim {{Ca}\frac{\mu_{0}}{\mu_{w}}}} & (15)\end{matrix}$

The datasets shown in FIG. 3(a) were organized according to Eq.(15)above and were found to collapse onto a single curve (FIG. 3(d)),demonstrating that the above scaling model captures the essentialphysics of the phenomenon: the gravitational potential energy of therolling droplet is primarily consumed in viscous dissipation in thewetting ridge around the base of the rolling droplet. Furthermore,Eq.(14) and Eq.(15) apply for cloaked and uncloaked droplets, becauseinertial and gravitational forces in the cloaking films are very small.Consequently, the velocity is uniform across the film and viscousdissipation is negligible.

Droplets placed on lubricant-impregnated surfaces exhibit fundamentallydifferent behavior compared to typical superhydrophobic surfaces. Insome embodiments, these four-phase systems can have up to threedifferent three-phase contact lines, giving up to twelve differentthermodynamic configurations. In some embodiments, the lubricant filmencapsulating the texture is stable only if it wets the texturecompletely (θ=0), otherwise portions of the textures dewet and emergefrom the lubricant film. In some embodiments, complete encapsulation ofthe texture is desirable in order to eliminate pinning. In someembodiments, texture geometry and hierarchical features can be exploitedto reduce the emergent areas and achieve roll-off angles close to thoseobtained with fully wetting lubricants. In some embodiments, droplets oflow-viscosity liquids, such as water placed on these impregnatedsurfaces, roll rather than slip with velocities that vary inversely withlubricant viscosity. In some embodiments, additional parameters, such asdroplet and texture size, as well as the substrate tilt angle, may bemodeled to achieve desired droplet (and/or other substance) movement(e.g., rolling) properties and/or to deliver optimal non-wettingproperties.

FIG. 4 is a schematic describing six liquid-impregnated surface wettingstates, in accordance with certain embodiments described herein. The sixsurface wetting states (state 1 through state 6) depend on the fourwetting conditions shown at the bottom of FIG. 4 (conditions 1 to 4). Insome embodiments, the non-wetted states are preferred (states 1 to 4).Additionally, where a thin film stably forms on the tops of the posts(or other features on the surface), as in non-wetted states 1 and 3,even more preferable non-wetting properties (and other relatedproperties described herein) may be observed.

In order to achieve non-wetted states, it is often preferable to havelow solid surface energy and low surface energy of the impregnatedliquid compared to the nonwetted liquid. For example, surface energiesbelow about 25 mJ/m² are desired in some embodiments. Low surface energyliquids include certain hydrocarbon and fluorocarbon-based liquids, forexample, silicone oil, perfluorocarbon liquids, perfluorinated vacuumoils (e.g., Krytox 1506 or Fromblin 06/6), fluorinated coolants such asperfluoro-tripentylamine (e.g., FC-70, sold by 3M, or FC-43),fluorinated ionic liquids that are immiscible with water, silicone oilscomprising PDMS, and fluorinated silicone oils.

Examples of low surface energy solids include the following: silanesterminating in a hydrocarbon chain (such as octadecyltrichlorosilane),silanes terminating in a fluorocarbon chain (e.g., fluorosilane), thiolsterminating in a hydrocarbon chain (such butanethiol), and thiolsterminating in a fluorocarbon chain (e.g. perfluorodecane thiol). Incertain embodiments, the surface comprises a low surface energy solidsuch as a fluoropolymer, for example, a silsesquioxane such asfluorodecyl polyhedral oligomeric silsesquioxane. In certainembodiments, the fluoropolymer is (or comprises) tetrafluoroethylene(ETFE), fluorinated ethylenepropylene copolymer (FEP), polyvinylidenefluoride (PVDF), perfluoroalkoxytetrafluoroethylene copolymer (PFA),polytetrafluoroethylene (PTFE), tetrafluoroethylene,perfluoromethylvinylether copolymer (MFA),ethylenechlorotrifluoroethylene copolymer (ECTFE),ethylene-tetrafluoroethylene copolymer (ETFE), perfluoropolyether, orTecnoflon.

In FIG. 4, γ_wv is the surface energy of the non-wetted phase inequilibrium with vapor; γ_(ow) is the interfacial energy between thenon-wetted phase and the impregnated liquid; γ_(ov) is the surfaceenergy of the impregnated liquid phase in equilibrium with vapor, γ_(sv)is the surface energy of the solid in equilibrium with vapor, γ_(so) isthe interfacial energy between the impregnated phase and the solid;γ_(sw) is the interfacial energy between the solid and the non-wettedphase; r=total surface area divided by projected surface area; Θ_(c1),Θ_(c2), Θ_(c3), Θ_(c4), Θ_(w1), Θ_(w2), are the macroscopic contactangles made by the non-wetted phase in each wetting state; Θ*_(os(v)) isthe macroscopic contact angle of oil on the textured substrate when thephase surrounding the textured substrate is vapor; Θ_(os(v)) is thecontact angle of oil on a smooth solid substrate of the same chemistrywhen the phase surrounding the oil droplet is vapor; Θ*_(os(w)) is themacroscopic contact angle of oil on the textured substrate when thephase surrounding the oil droplet is water; and Θ_(os(w)) is the contactangle of oil on a smooth substrate of the same chemistry as the texturedsurface when the phase surrounding the oil droplet is water.

FIG. 5 is a schematic showing conditions for the six liquid-impregnatedsurface wetting states shown in FIG. 4, in accordance with certainembodiments of the invention.

In certain embodiments, lubricant cloaking is desirable and is used ameans for preventing environmental contamination, like a time capsulepreserving the contents of the cloaked material. Cloaking can result inencasing of the material thereby cutting its access from theenvironment. This can be used for transporting materials (such asbioassays) across a length in a way that the material is notcontaminated by the environment.

In certain embodiments, the amount of cloaking can be controlled byvarious lubricant properties such as viscosity, surface tension.Additionally or alternatively, the de-wetting of the cloaked material torelease the material may be controlled. Thus, it is contemplated that asystem in which a liquid is dispensed in the lubricating medium at oneend, and upon reaching the other end is exposed to environment thatcauses the lubricant to uncloak.

In certain embodiments, an impregnating liquid is or comprises an ionicliquid. Ionic liquids have extremely low vapor pressures ˜(10⁻¹² mmHg),and therefore they mitigate the concern of the lubricant loss throughevaporation. In some embodiments, an impregnating liquid can be selectedto have a S_(ow(a)) less than 0. Exemplary impregnating liquids include,but are not limited to, tetrachloroethylene (perchloroethylene), phenylisothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene,o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene,acetylene tetrabromide, 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl) imide (BMIm), tribromohydrin(1,2,3-tribromopropane), tetradecane, cyclohexane, ethylene dibromide,carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax,Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene,perchloroethylene, carbon disulfide, phenyl mustard oil,monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide,aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleicacid, linoleic acid, amyl phthalate and any combination thereof.

In accordance with the present invention, exemplary solid featuresinclude, but are not limited to, polymeric solid, a ceramic solid, afluorinated solid, an intermetallic solid, and a composite solid and anycombination thereof. As demonstrated in FIG. 1, solid features cancomprise any suitable shapes and/or define any suitable structures.Exemplary solid features include, but are not limited to, pores,cavities, wells, interconnected pores, and interconnected cavities andany combination thereof.

In some embodiments, solid features have a roughened surface. As usedherein, θ_(os(a))(is defined as the contact angle of oil (subscript ‘o’)on the textured solid (subscript ‘s’) in the presence of air (subscript‘a’). In certain embodiments, the roughened surface of solid featuresprovides stable impregnation of liquid therebetween or therewithin, whenθ_(os(v))>θ_(c).

In certain embodiments, liquid-impregnated surfaces described hereinhave advantageous droplet roll-off properties that minimize theaccumulation of the contacting liquid on the surfaces. Without beingbound to any particular theory, a roll-off angle α of theliquid-impregnated surface in certain embodiments is less than 50°, lessthan 40°, less than 30°, less than 25°, or less than 20°.

Typically, flow through a pipe or channel, having an liquid-impregnatesurface on its interior may be modeled according to Eq. (14):

$\begin{matrix}{\frac{Q}{\Delta\;{p/L}} \sim {\left( \frac{R^{4}}{\mu_{1}} \right)\left\lbrack {1 + {\left( \frac{h}{R} \right)\left( \frac{\mu_{1}}{\mu_{2}} \right)}} \right\rbrack}} & (14)\end{matrix}$where Q is the volumetric flow rate, R is pipe radius, h is the heightof the texture, μ₂ is the viscosity of lubricant and μ₁ is the viscosityof the fluid flowing through the pipe. Δp/L is the pressure drop per L.Without being bound to any particular theory, it is believed that(h/R)(μ₁/μ₂) is greater than 1 for this to have a significant effect andthis sets the height of the texture in relation to the viscosity ratio.

Although modeled for pipe flow, the general principals also apply toopen systems, where R is replaced with the characteristic depth of theflowing material. The average velocity of the flow ˜Q/A, where A is thecross-sectional area of the flowing fluid.

For example, mayonnaise has a viscosity that approaches infinity at lowshear rates (it is a Bingham plastic (a type of non-Newtonianmaterial)), and therefore behaves like a solid as long as shear stresswithin it remains below a critical value. Whereas, for honey, which isNewtonian, the flow is much slower. For both systems, h and R are of thesame order of magnitude, and μ₂ is the same. However, sinceμ_(honey)<<μ_(mayonnaise), then

$\begin{matrix}{{\left( \frac{h}{R} \right)\left( \frac{\mu_{honey}}{\mu_{2}} \right)} ⪡ {\left( \frac{h}{R} \right)\left( \frac{\mu_{mayonnaise}}{\mu_{2}} \right)}} & (15)\end{matrix}$

thus mayonnaise flows much more quickly out of the bottle than honey.

According to some embodiments of the present invention, an articleincludes an interior surface, which is at least partially enclosed(e.g., the article is an oil pipeline, other pipeline, consumer productcontainer, other container) and adapted for containing or transferring afluid of viscosity μ₁, wherein the interior surface comprises aliquid-impregnated surface, said liquid-impregnated surface comprisingan impregnating liquid and a matrix of solid features spacedsufficiently close to stably contain the impregnating liquidtherebetween or therewithin, wherein the impregnating liquid compriseswater (having viscosity μ₂). In certain embodiments, μ1/μ2 is greaterthan about 1, about 0.5, or about 0.1.

In certain embodiments, the impregnating liquid comprises an additive toprevent or reduce evaporation of the impregnating liquid. The additivecan be a surfactant. Exemplary surfactants include, but are not limitedto, docosanoic acid, trans-13-docosenoic acid, cis-13-docosenoic acid,nonylphenoxy tri(ethyleneoxy) ethanol, methyl 12-hydroxyoctadecanate,1-Tetracosanol, fluorochemical “L-1006”, and combination thereof. Moredetails can be found in White, Ian. “Effect of Surfactants on theEvaporation of Water Close to 100 C.” Industrial & Engineering ChemistryFundamentals 15.1 (1976): 53-59, the contents of which are incorporatedherein by references. In addition or alternative, exemplary additivescan be C₁₆H₃₃COOH, C₁₇H₃₃COOH, C₁₈H₃₃COOH, C₁₉H₃₃COOH, C₁₄H₂₉OH,C₁₆H₃₃OH, C₁₈H₃₇OH, C₂₀H₄₁OH, C₂₂H₄₅OH, C₁₇H₃₅COOCH₃, C₁₅H₃₁COOC₂H₅,C₁₆H₃₃OC₂H₄OH, C₁₈H₃₇OC₂H₄OH, C₂₀H₄₁OC₂H₄OH, C₂₂H₄₅OC₂H₄OH, Sodiumdocosyl sulfate, poly(vinyl stearate), Poly(octadecyl acrylate),Poly(octadecyl methacrylate) and combination thereof. More details canbe found in Barnes, Geoff T. “The potential for monolayers to reduce theevaporation of water from large water storages.” Agricultural WaterManagement 95.4 (2008): 339-353, the contents of which are incorporatedherein by references.

EXPERIMENTAL EXAMPLES Example 1

FIG. 6 shows experimental measurements of water droplet mobility onliquid impregnating surfaces. FIG. 6a is a plot of roll-off angle α as afunction of emerged area fraction ϕ, for different surfaces (featurespacing b varies). An ionic liquid (1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl) imide (BMIm) was used as a impregnatingliquid in this work. The top inset (FIG. 6b ) shows an SEM image of theBMIm impregnated texture and shows that the post tops are dry. In FIG.6c , when the posts are further roughened by adding nanograss, they arecovered with BMIm (bottom inset) and consequently, the roll-off angledecreases.

The experiments of FIG. 6 demonstrate that liquid-impregnated surfacescan be engineered to provide resistance to impalement and to providenon-wettability, without requiring replenishment of impregnating fluidto make up for liquid lost to cloaking (BMIm is an example liquid thatdoes not cloak in the presence of air and water), and without requiringreplenishment of impregnating liquid to maintain coverage over the topsof the solid features.

BMIm impregnated textures showed roll-off angles that increase as thespacing decreases. This observation shows that pinning is non-negligiblein this case, and occurs on the emergent post tops (FIG. 6b ). However,this pinning was significantly reduced by adding a second smaller lengthscale texture (i.e. nanograss on the posts), so that BMIm impregnatedthe texture even on the post tops, thereby substantially reducing ϕ(though still non-zero) (see FIG. 6c ). It is important to note that thereduction in the emergent area fraction ϕ is not due to the absolutesize of the texture features; since the oil-water and oil-air interfacestypically intersect surface features at contact angles θ_(os(w)) andθ_(ow(a)), ϕ rather depends on these contact angles and featuregeometry.

Example 2

This Example demonstrates that condensation can be inhibited bypreventing coalescence due to liquid cloaking.

FIG. 7(a) shows an ESEM image sequence of condensation on a micropostsurface impregnated with Krytox that has positive spreading coefficienton water (S_(ow)>0). Condensation is inhibited as Krytox cloaks thecondensed droplets. FIG. 7(b) illustrates cloaked condensate dropletdepicting the thin film of condensate that spreads on the droplet. FIG.7(c) shows an ESEM image sequence of condensation on micropost surfaceimpregnated with BMIm that has negative spreading coefficient with water(S_(ow)<0). FIG. 7(b) illustrates uncloaked condensate droplet depictingthe three phase contact line of the water-vapor, water-lubricant, andlubricant-vapor interfaces on one end and pinning of the droplet at thedry post tops at the other end. FIG. 7(e) is a plot comparing variationof surface area fraction covered by condensed water droplets versus timeon surfaces impregnated with Krytox (S_(ow)>0, solid squares) and BMIm(S_(ow)<0, open diamonds). FIG. 7(f) is a plot comparing number of waterdroplets per unit area versus time on surfaces impregnated with Krytox(solid squares) and BMIm (open diamonds). The ESEM experiments wereconducted under identical conditions (pressure=800 Pa, substratetemperature ˜3.6° C., beam voltage=25 kV and beam current=1.7 nA). Inthe analysis, t=0 s is defined as the first frame in which water dropscan be identified.

Referring to FIG. 8, the very high subcooling is sufficient forcondensation rate to overcome the cloaking phenomenon for 10 cSt oil.The temperature of the peltier cooler was set at −5° C. The roomtemperature was 20° C., and the dew point in the conditions was 12° C.However, the barrier for coalescence is significantly higher on moreviscous lubricant even at this high degree of subcooling. As a result,the droplets appear on 10 cSt oil as hemispherical shapes, whereas onmore viscous lubricant their sphericity is significantly lower.

Example 3

This Example demonstrates that condensation is inhibited by thedecreased drainage rate of oil between neighboring water droplets,particularly where the oil has high viscosity.

Similar to the conditions described in Example 2, the temperature of thepeltier cooler was set at −5° C. The room temperature was 20° C., andthe dew point in the conditions was 12° C. As can be seen in FIG. 9, thecondensation growth rate is significantly decreased as viscosity of theoil increases. Upon condensation on liquid-impregnated surfaces withS_(ow)>0, coalescence is significantly inhibited because of the presenceof the cloaking oil film between droplets. As viscosity of the oilincreases, the force required to drain the oil film between twoneighboring droplets also increases and hence condensation/frost growthis inhibited. Further, the more viscous an oil, the less rapid thedeformation of its surface upon adsorption of vapor molecules, and thismay reduce the rate of formation of condensed droplets, as well.

Example 4

This Example demonstrates that frost can be inhibited by decreasing thedrainage rate of oil from condensed structures, particularly where theoil has high viscosity.

Similar to the conditions described above, the temperature of thepeltier cooler was set at −15° C. The experiments were conducted in lowrelative humidity environment such that the dew point in theseconditions was −10° C. In these conditions, water vapor forms directlyas frost on the peltier plate. However, on the impregnated surface,water vapor still forms as droplets, and frost. As can be seen in FIG.10, the frost formation rate is significantly decreased as viscosity ofthe oil increases. On low viscosity liquid, the water phase showsmobility signifying that water exists as supercooled droplets.

Example 5

This example demonstrates results of a series of experiments thatincluded flowing a number of different external phases on a number ofdifferent solid surfaces impregnated with different impregnatingliquids. The results of the conducted experiments are shown in Table 1below. In Table 1 below, θ_(os(a),receding) is the receding contactangle of the impregnating liquid (e.g., silicone oil, subscript ‘o’) onthe surface (subscript ‘s’) in the presence of air (subscript ‘a’), andwhere θ_(os(e),receding) is the receding contact angle of theimpregnating liquid (e.g., silicone oil, subscript ‘o’) on the surface(subscript ‘s’) in the presence of the external phase (subscript ‘e’).θ*_(c)=Cos⁻¹(1/r) is the critical contact angle on the texturedsubstrate and α* is the roll-off angle.

TABLE 1 Experimental determination of roll-off angles. Cos⁻¹(1/r) =θ_(os(a),receding) , External Impregnating Θ_(os(a),receding)θ_(os(e),receding) θ_(c) ^(*) θ_(os(e),receding) < α^(*) phase (e) Solid(s) liquid (o) ( ° ) ( ° ) ( ° ) θ^(*) _(c) ( ° ) Mayonnaise CW PDC 0 3747 Yes 5 Toothpaste CW PDC 0 25 47 Yes 3 Toothpaste WPTFE PDC 20 67 50No 45 WB Paint WPTFE PDC 20 67 50 No 65 WB Paint WPTFE Krytox 1506 2 3550 Yes 15 Peanut WPTFE PDC 20 90 50 No 70 Butter Peanut WPTFE CL 5 35 50Yes 20 Butter DI Water OTS- Silicone oil 0 0 60 Yes ~1 treated siliconDI Water Silicon Silicone oil 0 122 60 No Did not roll off, even at 90°

Slide off angles were measured using 500 μL volumes of the externalfluid, except for water, for which 5 μL droplets were used. It wasobserved that in experiments where θ_(os(e),rec)<θ*_(c), the roll-offangles, α*, were low (e.g., less than or equal to 20°), whereas in caseswhere θ_(rec,os(e))>θ*_(c), the roll-off angles, α*, were high (e.g.,greater than or equal to 40°).

The silicon surfaces used in the experimental data shown in Table 1above were 10 m square silicon posts (10×10×10 μm) with 10 m interpillarspacing. The 10 m square silicon microposts were patterned usingphotolithographic and etched using deep reactive ion etching (DRIE). Thetextured substrates were cleaned using piranha solution and were coatedwith octadecyltrichlorosilane (OTS from Sigma-Aldrich) using a solutiondeposition method.

The “WPTFE” surfaces shown in Table 1 above were composed of a 7:1spray-coated mixture of a mixture of Teflon particles and Toko LF DiblocWax, sprayed onto a PET substrate. The carnauba wax (CW) surfaces werecomposed of PPE CW spray-coated onto a PET substrate. The impregnatingliquids were propylene di(caprylate/caprate) (“PDC”), Krytox 1506, DOWPMX 200 silicone, oil, 10 cSt (“Silicone oil”) and Christo-lube EXP101413-1 (“CL”). The external phases used were mayonnaise, toothpaste(e.g., Crest extra whitening), and red water based paint. Wenzelroughness, r, was measured using a Taylor hobson inferometer. Althoughprecise estimates of ϕ could not be easily obtained, it was observed inthe inferometer that ϕ was much less than 0.25 for all the impregnatedsurfaces described in the table, and tested, and using 0.25 as an upperbound on ϕ for our surfaces we determine that cos⁻¹(1−ϕ)/(r−ϕ)=θ_(c) isno more than 5° greater than the values for θ*_(c).

Materials and Methods—Lubricant-Impregnated Surfaces

The textured substrates used in the examples discussed below were squaremicroposts etched in silicon using standard photolithography process;these square microposts are shown in FIG. 12(a). A photomask with squarewindows was used and the pattern was transferred to photoresist using UVlight exposure. Next, reactive ion etching in inductively-coupled plasmawas used to etch the exposed areas to form microposts. Each microposthad a square geometry with width a=10 μm, height h=10 μm, and varyingedge-to-edge spacing b=5, 10, 25, and 50 μm.

A second level of roughness was produced on microposts in someembodiments by creating nanograss, as shown in the SEM image of FIG.12(b). For this purpose, Piranha-cleaned micropost surfaces were etchedin alternating flow of SF₆ and O₂ gases for 10 minutes ininductively-coupled plasma.

The samples were then cleaned in a Piranha solution and treated with alow-energy silane (octadecyltrichlorosilane—OTS) by solution deposition.The samples were impregnated with lubricant by slowly dipping them intoa reservoir of the lubricant. They were then withdrawn at speed S slowenough that capillary numbers Ca=μ_(o)S/γ_(oa)<10⁻⁵ to ensure that noexcess fluid remained on the micropost tops where μ_(o) is the dynamicviscosity and γ_(oa) is the surface tension of the lubricant. In someembodiments, when the advancing angle θ_(adv,os(a)) is less than θ_(c)(see Table 4 below) the lubricant film will not spontaneously spreadinto the textured surface, as can be seen for BMIm(1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) in FIG.13. However, by withdrawing the textured surfaces from a reservoir ofBMIm, the impregnating film remains stable, since θ_(rec,os(a))<θ_(c)for the microposts with b=5 μm and 10 μm.

Laser Confocal Fluorescence Microscope (LCFM) Imaging

In order to determine whether or not the micropost tops were coveredwith lubricant after dipping, a LCFM (Olympus FV 300) was used. Aflorescent dye (DFSB-175, Risk Reactor, CA) was dissolved in thelubricant, and the textured substrate was impregnated with the dyedlubricant using dip coating, as explained above. The dye gets excited atwavelengths of ˜400 nm, and the resulting emittance was captured by themicroscope. In some embodiments, as the focused laser beam scannedthrough the sample, areas containing dye appeared bright, indicating thepresence of lubricant. This is shown, for example, in FIG. 1(g) onsubstrates impregnated with silicone oil. In contrast, in someembodiments, BMIm does not wet post tops, which therefore appear dark,as shown, for example, in (FIG. 1(h)). Contact angle measurements

Contact angles of silicone oil and BMIm were measured on the OTS-coatedsilicon surfaces in the presence of air and DI water using a Ramé-HartModel 500 Advanced Goniometer/Tensiometer. The advancing (θ_(adv,os(a)),θ_(adv,os(w))) and receding (θ_(rec,os(a)), θ_(rec,os(w))) angles weretaken as an average of at least 8 measurements. 5 μl droplets weredeposited at a volume addition/subtraction rate of 0.2 μl s⁻¹, yielding,in some embodiments, contact line velocities V_(c) less than 1 mm min⁻¹.The resulting capillary numbers were Ca=μ_(o)V_(c)/γ_(o(i))<10⁻⁵ensuring that the measured dynamic contact angles were essentially thesame as contact angles obtained immediately after the contact line comesto rest. The measured contact angles are shown in Table 2 below.

Table 2 shows contact angle measurements on smooth OTS-treated siliconsurfaces. In some embodiments, a surface that has been dipped insilicone oil maintains an oil film on the surface after a water dropletis deposited because the film cannot dewet the surface sinceθ_(rec,os(w))=0°. Therefore, an oil-water-solid contact line cannotexist and pinning forces must be zero. Accordingly, the oil-solid-waterpinning term in Eq.'s (10) and (11) above should be neglected ifθ_(rec,os(w))=0°. Similarly oil-solid-air pinning term should beneglected if θ_(rec,os(a))=0°. For this reason, pinning forces are takento be zero in FIG. 11(a)-(d) for silicone oil, even though cosθ_(rec,os(w))−cos θ_(adv,os(w))>0.

TABLE 2 Contact Angle Measurements on Smooth OTS-Treated SiliconSurfaces. Liquid Substrate θ_(adv,os(a)) (°) θ_(rec,os(a)) (°)θ_(adv,os(w)) (°) θ_(rec,os(w)) (°) Silicone oil OTS-treated 0 0   20 ±5 0 silicon BMIm OTS treated  67.8 ± 0.3 60.8 ± 1.0  61.3 ± 3.6  12.5 ±4.5 silicon DI water OTS-treated 112.5 ± 0.6 95.8 ± 0.5 NA NA siliconSilicone oil Silicon 0 0 153.8 ± 1.0   122 ± 0.8 BMIm Silicon  23.5 ±1.8  9.8 ± 0.9 143.4 ± 1.8 133.1 ± 0.9 DI water Silicon   20 ± 5° 0 NANA

Table 3 shows surface and interfacial tension measurements and resultingspreading coefficients, S_(ow(a))=γ_(wa)−γ_(ow)−γ_(oa), of 9.34, 96.4,and 970 cP Dow Corning PMX 200 Silicone oils on water in air. Values ofγ_(ow) for silicone oil were taken from C. Y. Wang, R. V. Calabrese,AIChE J. 1986, 32, 667, in which the authors made measurements using thedu Noüy ring method (described in du Noüy, P. Lecomte. “An interfacialtensiometer for universal use.” The Journal of general physiology 7.5(1925): 625-631), and values of γ_(oa) were provided by Dow Corning. Thesurface and interfacial tensions for BMIm and Krytox were measured usingthe pendant drop method (described in Stauffer, C. E., The measurementof surface tension by the pendant drop technique. J. Phys. Chem. 1965,69, 1933-1938). Here, γ_(wa), γ_(ow), and γ_(oa) are the surface andinterfacial tensions between phases at equilibrium, that is, after waterand the lubricant become mutually saturated.

TABLE 3 Surface and Interfacial Tension Measurements and ResultingSpreading Coefficients Liquid γ_(ow)(mN/m) γ_(oa) (mN/m) γ_(wa) (mN/M)S_(ow(a)) (mN/m) Silicone oil 46.7 20.1 72.2 5.4 (9.34 cP, 96.4 cP)Silicone oil 45.1 21.2 72.2 5.9 (970 cP) Krytox 49 17 72.2 6 Ionicliquid 13 34 42 −5

Table 4 shows texture parameters b, r, ϕ, and critical contact anglesθ_(c) defined by θ_(c)=cos⁻¹((1−ϕ)/(r−ϕ)), and θ*_(c)=cos⁻¹(1/r); h,a=10 μm for all substrates tested. The approximation θ_(c)≈θ*_(c),becomes more accurate as ϕ approaches zero. If the silicon substrate isnot coated with OTS, θ_(os(w))>θ_(c), θ*_(c) for both lubricants and allb values. Thus, water droplets should displace the lubricant and getimpaled by the microposts leading to significant pinning, which wasconfirmed experimentally, as it was observed that such droplets did notroll-off of these surfaces.

TABLE 4 Texture Parameters and Critical Angles. Post spacing, b (μm) r ϕθ_(c) (°) θ*_(c) (°) 5 2.8 0.44 76 69 7.5 2.3 0.33 70 64 10 2.0 0.25 6560 25 1.3 0.08 42 41 50 1.1 .093 26 26

EQUIVALENTS

While the invention has been particularly shown and described withreference to specific preferred embodiments, it should be understood bythose skilled in the art that various changes in form and detail may bemade therein without departing from the spirit and scope of theinvention as defined by the appended claims.

What is claimed is:
 1. An article comprising a liquid-impregnatedsurface, said surface comprising an impregnating liquid and a matrix ofsolid features spaced sufficiently close to stably contain theimpregnating liquid therebetween or therewithin, wherein one or both ofthe following holds: (i) θ_(os(e),receding) =0; and (ii)θ_(os(v),receding) =0 and θ_(os(e),receding) =0, whereθ_(os(e),receding) is receding contact angle of the impregnating liquidon the surface (subscript ‘s’) in the presence of a non-vapor (e.g.,liquid, solid, semi-solid, gel) phase external to the surface that isdifferent from the impregnating liquid (subscript ‘e’), and whereθ_(os(v),receding) is receding contact angle of the impregnating liquid(e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in thepresence of vapor phase (subscript ‘v’, e.g., air).
 2. The article ofclaim 1, further comprising material of said non-vapor phase external tosaid surface (and in contact with said surface), said article containingsaid non-vapor phase material.
 3. The article of claim 2, wherein saidmaterial of said non-vapor phase external to said surface comprises oneor more of the following: food, cosmetic, cement, asphalt, tar, icecream, egg yolk, water, alcohol, mercury, gallium, refrigerant,toothpaste, paint, peanut butter, jelly, jam, mayonnaise, ketchup,mustard, condiment, laundry detergent, consumer product, gasoline,petroleum product, oil, biological fluid, blood, plasma.
 4. The articleof claim 1, wherein the article is a container, a pipeline, a nozzle, avalve, a conduit, a vessel, a bottle, a mold, a die, a chute, a bowl, atub, a bin, a cap, and/or a tube.
 5. The article of claim 1, whereinθ_(os(e),receding)=0.
 6. The article of claim 1, wherein the articlecomprises an interior surface that is at least partially enclosed, theinterior surface containing or transferring the phase external to thesurface and having a viscosity μ₁, wherein the interior surfacecomprises the liquid-impregnated surface, wherein the impregnatingliquid is aqueous (having viscosity μ₂).
 7. The article of claim 6,wherein the article is a member selected from the group consisting of apipeline, a steam turbine part, a gas turbine part, an aircraft part, awind turbine part, eyeglasses, a mirror, a power transmission line, acontainer, a windshield, an engine part, tube, nozzle, or a portion orcoating thereof.
 8. The article of claim 6, wherein μ₁ / μ₂>0.1.
 9. Thearticle of claim 6, wherein the impregnating liquid comprises anadditive (e.g., a surfactant) to prevent or reduce evaporation of theimpregnating liquid.
 10. The article of claim 1, wherein theimpregnating liquid comprises at least one member selected from thegroup consisting of silicone oil, propylene glycoldicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin (PAO),synthetic hydrocarbon cooligomer, fluorinated polysiloxane, propyleneglycol, tetrachloroethylene (perchloroethylene), phenyl isothiocyanate(phenyl mustard oil), bromobenzene, iodobenzene, o-bromotoluene,alpha-chloronaphthalene, alpha-bromonaphthalene, acetylene tetrabromide,1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm),tribromohydrin (1,2,3-tribromopropane), ethylene dibromide, carbondisulfide, bromoform, methylene iodide (diiodomethane), stanolax,Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene,perchloroethylene, carbon disulfide, phenyl mustard oil,monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide,aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleicacid, linoleic acid, and amyl phthalate.